![](bg7.png)
rounds and multiplications to evaluate the communi-
cation costs of the protocols.
In comparison protocols, for the sake of simplic-
ity, we assume that the compared values are restricted
to less than
p−1
2
and p = 2
l
−c, where c is a small
integer. Therefore, only one attempt is required to
compute r < p in RBVS protocol. In interval test
protocols, inputs are arbitrary values in Z
p
, and two
attempts are required.
Table 1: Complexities of comparison protocols.
Rounds Multiplications
(Damg
˚
ard et al., 2006) 44 148l + 188llog
2
l
(Nishide and Ohta, 2007) 13 36l + 1
(Reistad and Toft, 2007) 8 20l + 36llog
2
l + 6
(Reistad, 2009) 6 7.5l + 11
Proposed 5 (6 + 5/6)l + 3
Table 2: Complexities of interval test protocols.
Rounds Multiplications
(Nishide and Ohta, 2007) 13 72l + 1
Proposed 5 (24+ 5/3)l + 9
7 CONCLUSIONS
The main results obtained in this study are as follows.
• By using a shuffling protocol, we proposed a five-
round secure comparison protocol .
• We constructed a five-round secure interval test
protocol by applying our secure comparison pro-
tocol.
• We showed that proposed protocols have less
communication costs than existing protocols.
In future studies, we will consider methods to further
reduce the communication costs of our protocols.
REFERENCES
Catrina, O. and De Hoogh, S. (2010). Improved primitives
for secure multiparty integer computation. In Interna-
tional Conference on Security and Cryptography for
Networks, pages 182–199. Springer.
Chida, K., Hamada, K., Ikarashi, D., Kikuchi, R., Kiribuchi,
N., and Pinkas, B. (2019). An efficient secure three-
party sorting protocol with an honest majority. Cryp-
tology ePrint Archive, Report 2019/695.
Cramer, R., Damg
˚
ard, I., and Ishai, Y. (2005). Share conver-
sion, pseudorandom secret-sharing and applications to
secure computation. In Theory of Cryptography Con-
ference, pages 342–362. Springer.
Damg
˚
ard, I., Fitzi, M., Kiltz, E., Nielsen, J. B., and Toft,
T. (2006). Unconditionally secure constant-rounds
multi-party computation for equality, comparison, bits
and exponentiation. In Theory of Cryptography Con-
ference, pages 285–304. Springer.
Damg
˚
ard, I., Geisler, M., and Krøigaard, M. (2007). Effi-
cient and secure comparison for on-line auctions. In
Australasian Conference on Information Security and
Privacy, pages 416–430. Springer.
Garay, J., Schoenmakers, B., and Villegas, J. (2007). Prac-
tical and secure solutions for integer comparison. In
International Workshop on Public Key Cryptography,
pages 330–342. Springer.
Gennaro, R., Rabin, M. O., and Rabin, T. (1998). Simpli-
fied vss and fast-track multiparty computations with
applications to threshold cryptography. In podc, vol-
ume 98, pages 101–111. Citeseer.
Laur, S., Willemson, J., and Zhang, B. (2011). Round-
efficient oblivious database manipulation. In Proceed-
ings of the 14th International Conference on Informa-
tion Security, ISC’11, pages 262–277, Berlin, Heidel-
berg. Springer-Verlag.
Morita, H., Attrapadung, N., Teruya, T., Ohata, S., Nuida,
K., and Hanaoka, G. (2018). Constant-round client-
aided secure comparison protocol. In ESORICS.
Nishide, T. and Ohta, K. (2007). Multiparty computa-
tion for interval, equality, and comparison without
bit-decomposition protocol. In International Work-
shop on Public Key Cryptography, pages 343–360.
Springer.
Reistad, T. I. (2009). Multiparty comparison-an improved
multiparty protocol for comparison of secret-shared
values. In SECRYPT, pages 325–330.
Reistad, T. I. and Toft, T. (2007). Secret sharing compar-
ison by transformation and rotation. In International
Conference on Information Theoretic Security, pages
169–180. Springer.
Shamir, A. (1979). How to share a secret. Communications
of the ACM, 22(11):612–613.
Veugen, T. (2012). Improving the dgk comparison protocol.
In 2012 IEEE International Workshop on Information
Forensics and Security (WIFS), pages 49–54. IEEE.
ICISSP 2020 - 6th International Conference on Information Systems Security and Privacy
704